What is (\partial)/(\partial x)(5*(y+4)*(x-2)^3) ?

The answer to (\partial)/(\partial x)(5*(y+4)*(x-2)^3) is 15(y+4)(x-2)^2

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(\partial)/(\partial x)(5(y+4)(x-2)^3)

\frac{\partial}{\partial x} (5 \cdot (y + 4) \cdot (x - 2)^{3})

15 (y + 4) (x - 2)^{2}

Solution steps

\frac{\partial}{\partial x} (5 (y + 4) (x - 2)^{3})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 (y + 4) \frac{\partial}{\partial x} ((x - 2)^{3})

Apply the chain rule:

3 (x - 2)^{2} \frac{\partial}{\partial x} (x - 2)

= 3 (x - 2)^{2} \frac{\partial}{\partial x} (x - 2)

\frac{\partial}{\partial x} (x - 2) = 1

= 5 (y + 4) \cdot 3 (x - 2)^{2} \cdot 1

Simplify

= 15 (y + 4) (x - 2)^{2}

\frac{\partial}{\partial y} ((x - y)^{2})

\frac{d}{d x} (\frac{4 x ^{2} + 3 x}{2 x - 7})

x \to 2 lim (- x^{3} + 3)

f (x) = x^{2} + 1, at x = 4

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What is (\partial)/(\partial x)(5*(y+4)*(x-2)^3) ?
The answer to (\partial)/(\partial x)(5*(y+4)*(x-2)^3) is 15(y+4)(x-2)^2